Interpreting Lincom in a Logistic Regression

[Amber Trueblood]

I am having a hard time interpreting a logistic regression after I used lincom to show 10% and 90% increases in my independent variables; the outcome is cluster vs non-cluster county.

The code I used after my regression was:

lincom variable1*0.10 and lincom variable1*0.90

I receive the Odds Ratios:

	Odds Ratio (OR)	95% CI	P-Value
10% Increase in Percentage Families Below Poverty	0.97	0.97,1.00	0.002
90% Increase in Percentage Families Below Poverty	0.88	0.85,0.97	0.002
*Actual Numbers Changed

But, I am having a hard time interpreting this. From my understanding this output shows that for a 10% increase in the Percentage of Families Below Poverty the odds for being a cluster county is 0.97 times lower. Whereas, for a 90% increase in the Percentage of Families Below Poverty the odds for being a cluster county were 0.88 times lower.

Does anyone know of a good reference to help with interpreting these findings? Or if there is another command besides lincom to try to explain continuous independent variables in Stata (all of my variables are percentages).

[Clyde Schechter]

The command

lincom variable1*0.10

calculates the 0.1 times the coefficient of variable1 in your model output. It doesn't calculate any odds ratio, or the odds ratio associated with any particular change in variable1 or any other variable.

I'm not entirely clear on what it is you want to do here, but it sounds more like a task for -margins-. But just how you would do that depends on the exact statement of the regression command itself (and might require revising that command), an explanation of what the variables in the regression command mean, and a clearer explanation of what you are trying to estimate.

[Amber Trueblood]

First, I ran a logistic regression with the outcome variable being cluster or non-cluster. I then did backwards selection with 40 variables to build a final model, but all of my variables are percentages (census data) (i.e. percent white, percent black, percent vacant structures, etc). The problem now is interpreting the findings.

Table 17 Multiple Logistic Regression for Cluster Counties for 2000-2006a
	Odds Ratio (OR)	95% CI	P-Value
Percent Black or African American	0.81	0.75,0.89	0.000

To help with interpretation I was directed to try using the lincom which we believed was showing a 10% and 90% increase in the variable.

Table 18 Multiple Logistic Regression for Cluster Counties for 2000-2006a
	Odds Ratio (OR)	95% CI	P-Value
10% Increase in the Percent Black or African American	0.98	0.97,0.98	0.000
90% Increase in the Percent Black or African American	0.83	0.77,0.90	0.000

Now, we are trying to interpret that.

I will look into margins to see if it will help with the issue I am having.

Thank you,
Amber

[Clyde Schechter]

Let me point out something else. In a non-linear model such as logistic regression, the effect of a 10% increase in a predictor variable will depend on what the baseline value of that predictor you reckon the 10% from is. Your question still does not seem clearly posed to me. But check out -margins-; I suspect it will do what you're looking for. I'm pretty sure -lincom- is not the right tool for this job.

[Amber Trueblood]

Thank you for your assistance. I will look into margins a bit more.

[Amber Trueblood]

I want to make sure I am understanding margins correctly.


. margins, at (PercentBlackAA=(0 5 10 15 20 25 30))

Predictive margins Number of obs = 254
Model VCE : OIM

Expression : Pr(ClusterCountyTime1), predict()

1._at : PercentBla~A = 0

2._at : PercentBla~A = 5

3._at : PercentBla~A = 10

4._at : PercentBla~A = 15

5._at : PercentBla~A = 20

6._at : PercentBla~A = 25

7._at : PercentBla~A = 30

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | .4519454 .048852 9.25 0.000 .3561974 .5476935
2 | .2628247 .02912 9.03 0.000 .2057506 .3198988
3 | .1258484 .0289677 4.34 0.000 .0690727 .1826241
4 | .0521916 .0222555 2.35 0.019 .0085717 .0958115
5 | .019952 .0128326 1.55 0.120 -.0051994 .0451033
6 | .0073396 .0063204 1.16 0.246 -.0050481 .0197272
7 | .0026571 .0028602 0.93 0.353 -.0029487 .008263
------------------------------------------------------------------------------


Based on my understanding by using 0% (1) as the comparison, counties with 5%(2) Black or African American population would be 58% more likely to be in a cluster compared to counties with 0% (1). In addition, counties with 10% (3) Black or African American population would be 28% more likely to be in a cluster compared to counties with 0%. Does that seem right to you or am I misunderstanding margins?

Thank you,
ABT

[Clyde Schechter]

The -margins- output is telling you that counties with PercentBlackAA = 0, the predicted probability of ClusterCountyTime1 is 0.45... For those counties with PercentBlackAA = 5, the predicted probability is 0.26... And so on. So it seems that as we look at counties with increasing PercentBlackAA, the probability of ClusterCountyTime1 is decreasing. If you take the ratio, of those two predicted probabilities, it tells us that counties with PercentBlackAA = 5 are 58% as likely to have ClusterCountyTime1 as counties with PercentBlackAA = 0. And so on.

I'm inferring from your wording that you expected this relationship to go in the opposite direction. Your logistic regression output itself, I imagine will show either a negative coefficient or an odds ratio < 1, corresponding to this decreasing relationship.

[Amber Trueblood]

Thank you for your help. Actually the trend I am seeing is actually what was expected for my outcome based on previous literature, so one positive as I try to finish this project.